We present soft X-ray variability timescales for 65 active galactic nuclei (AGNs) derived from ROSAT Position Sensitive Proportional Counter pointing data. For these 65 objects with obvious exponential increasing or decreasing patterns in their light curves, we use the exponential timescales and find they are more suitable for analyzing ROSAT light-curve data. We also discuss some physical constraints on the central engine implied by our results. Assuming that this soft X-ray variability exponential timescale is approximately equal to the thermal timescale of the standard accretion disk, we obtain the accretion rate, the size of the soft X-ray radiation region, and the compactness parameter for 37 AGNs, using their recently estimated central black hole masses. For 12 of these 37 AGNs, the radii of the gravitational instability in the standard thin accretion disks are obtained using the central black hole masses and the calculated accretion rates. These are consistent with the results from the reverberation mapping method. These results provide supporting evidence that such gravitational instabilities contribute to the formation of the broad-line regions in AGNs.
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